Liquid foam and soap film vibrations F. Elias, C. Derec, C. Gay, V. Leroy S. Hutzler, W. Drenckhan
Liquid foam and soap filmvibrations
F. Elias, C. Derec, C. Gay, V. Leroy
S. Hutzler, W. Drenckhan
To make a foam:To make a foam: water,air,soap.
water
air
Soap? Surfactant Soap? Surfactant moleculemolecule::
Hydrophobic tail
Hydrophilichead
Liquid Foams
Inside aInside asoap soap foamfoam::
Gas Bubblesseparated by aLiquid structured matrix
Internal structure
Liquid foam: poroelastic material with soft pores
Complex macroscopicproperties
Manipulate the foam with a wave -> new materials?
Why studying the Acoustics of Liquid Foams?
Measurements of(ultra)sound wave
velocity and attenuation over large range of
frequencies
characteristics of the foam (structure + composition)
Φ, <R>, …
?
Fundamental: investigate the dynamical properties of liquid foams
Probe the foam with ultrasounds.
! =Volume of the liquid phase
Volume of the foam
Average bubblesize
How does a foam modify the acoustic wave?
1. Acoustic properties of a liquid foam
2. Liquid foam in a standing wave
How does an acoustic wave change the foam?
Experimental studies
Setup :Setup :
1. Acoustic properties of a liquid foam; Preliminary results
c
L
S R
Source S :
Receptor R :
tf
time
1/f (f = 40 kHz)
Measurement of the flight time of an acoustic pulse in the foam
-> c =tf
L
<R> = 60 mm
v v stronglystrongly dependsdepends on on ΦΦ : :
Effective medium (Wood):
cg : sound velocity in thepure gas
0
100
200
300
0 0.1 0.2 0.3
c
(m/s)
!
Gaz: N2
Gaz: C2F6
344
170
!
2cg"g
"l
Φ = 1 v = vl = 1480 m/s
v
v vg
vg
UltrasoundsUltrasounds to to measuremeasure ΦΦ? ? MeasurementMeasurement withoutwithout contact: contact:
Dilatancy of foams
65 m
m
shear
Steps of shear rate
Rotorvelocity
Flight time of anacoustic pulse
50 100
Δtf
The foam is wetter in thesheared zon
Dilatancy : Φ increases when the shear rate increases.
0
0,5
1
1,5
2
2,5
3
3,5
0 1 2 3 4 5
y = 0,050535 + 0,77879x R2= 0,9988
Time of flight difference (
µs)
Plate velocity (rad/s)
0
1
2
3
Rotor velocity(rad/s)
Δtf (ms)
dilatance
tfcΦ
Emittertransducer
receiver
(S.P.L.Marze, A. Saint Jalmes, D. Langevin, Coll. Surf. A 2005)
A more complex problem… Acoustics of liquid foam in the literatureThe acoustic properties strongly depend on the liquid volume fraction (Φ)…
1 kHz
5 kHz
air+water+sulfone (3%) <R>= 1 mmair+water+??? <R> = 70-125 µmair+water+expandol(6%) <R> = 100-200 µmGillette <R> = 30 µm
chemical composition, mean radius, frequency
Φ Φ
… But it is not the only parameter
A broadband transducer emits a short pulse in air, which is reflected on thesample, and received by another transducer
Broadband characterisation:
emitter
FOAM
A0A
the complex impedance can be determined
From the reflection coefficient
Broadband characterisation:
mean reflection coefficient as a function of frequency
for v = 60 m/s
v = 55±10 m/s
Using shaving foam:
More experiments needed on foams with controlled physico-chemistry.
Allows to measure v but α is not easily measurable
γΔ
ε =dγdA
ε = 0ε ≠ 0 ε = ε’ + i ε’’
A
ω τ < 1ω τ > 1
Interfacial viscoelasticmodulus
area Surfacetension
The interfacial elasticity of the liquid matrix should be importantat high frequency
Soft elasticity of the liquid matrix:
τ
Soap film suspended on a vibrated frame
-> Dispersion relation?
air
air l = 2π / k
V
e
Inertia of theliquid film
Inertia of air
2 mm
Existing model:
Afenchenko et al, Phys. Fluids 10 (1998), 390
γ
Effect of the interfacial elasticity?
0
2
4
6
8
0 5 10 15 20
e = 3002 nme = 1312 nme = 830 nme = 607 nme = 432 nm
e = 342 nme = 299 nme = 245 nmv_modèle
et
with
-> Experiments: f = 300 Hz -> 10 kHz:
vexp > vtheory at high frequency
More experiments needed, and more theory.
Setup: Standing acoustic wave + « Bamboo » foam in a tube
Tube(plexyglas)
L = 2 m
35 mm
Loudspeaker
(f ~ 100 - 10 000 Hz)Soap films
Observation : white light illuminationlight reflected by soap films -> light interferences
2. What does an acoustic wave on a foam?Liquid Foam in a standing wave
Vibration of the soap films:Vibration of the soap films:
In the displacement antinodes:Vibration and swelling of the soapfilms
Soap filmundulation
VerticalTube
Counter-rotativevortices
Self-adaptationof the soapfilm localthickness
Visualisation of the standing wave:Visualisation of the standing wave:
820 Hz
1060 Hz
1300 Hz
1640 Hz
0
10
20
30
40
50
60
0 10 20 30 40 50 60
!
m
easure
d
(c
m)
! = c/f (cm)
λ = c/f(cm)
1
Conclusion
Bamboo foam in a standing wave
Acoustic properties of liquid foams
1- Strongly depends on the liquid content, but not only.2- Lack of theoretical modelling.3- Need experimental data with:
Large frequency range, Controlled bubble size (and polydispersity),
Controlled chemistry -> controlled interfacial viscoelasticity.
Acoustics: promising technique to probe the foam.
The response of the foam to an acoustic wave is complex!